Lesson # 56: The Fundamental Counting Principles

Investigate Counting without Counting:

example:    E        H       2
                 M   J   C       3
                  Y       P       2
2 x 3 x 2 = 12  (there are 12 possible meals)

The Fundamental Counting  Principle:
if one item can be selected in m ways, and for each way a second item can be selected in n ways, then the two items can be selected in m x n ways.

example part 1: how many different 2-digit numbers are there?
   9   x   10   = 90
1,2,3,4,5        0,1,2,3,4
6,7,8,9           5,6,7,8,9

example part 2: repetitions are not allowed.
   9   x   10   = 81
1,2,3,4,5        0.1.2.3.4
6,7,8,9           5,6,7,8,9

example: how many different patterns are possible for the answers to the 7 questions of the test (2 answers each)
2 x 2 x 2 x 2 x 2 x 2 x 2 = 1/128